The influence of the electromagnetic wave on the quantum acoustomagnetoelectric (QAME) field in a quantum well with a parabolic potential (QWPP) is investigated for an acoustic wave whose wavelength λ = 2π/q is smaller than the mean free path l of the electrons and in the region ql À 1 (where q is the acoustic wave number). The dependence of the QAME field E QAM E on the frequency of external acoustic wave ωq , the temperature T , the magnetic field B, the amplitude E0 and frequency Ω of the electromagnetic wave are obtained by using the quantum kinetic equation. Numerical calculation is done, and the result is discussed for a typical AlAs/GaAs/AlAs QWPP. The computational results show that the dependence of the QAME field E QAM E on the external acoustic wave frequency ωq , the frequency of electromagnetic wave Ω and the magnetic field B is non-monotonic, the cause of appearance peaks attributes the transition between mini-bands N → N 0 . The quantum theory of the QAME current in a QW is newly developed.